The book addresses the question of how logic relates to the psychology of reasoning. It is meant as an alternative to the Fregean view that psychology, being descriptive, is of no relevance to logic, given that the latter is normative. According to Frege, logic is concerned with how people should think rather than how they actually do think, the latter being the province of psychology. The authors defend what they describe as a Husserlian alternative to Frege, namely that logic is a mathematical ("theoretical") discipline. That is, "logic itself is a theoretical discipline, proving consequences of choices of parameters, and norms come from outside, by the choice of a particular logical form" (p. 352). Part of what this means is that logic is concerned with the descriptive question of what preserves truth. Frege was not correct in viewing norms as integral to logic, since normativity only enters in after the fact, in the judgment that truth is good.

Far more central to the book, however, is the authors' hypothesis that the mind imposes logical form on a task or puzzle ("choice of parameters"), the form consequently dictating the truth-preserving forms of inference. This is also a purely descriptive matter, and no qualms about norms arise. Logic provides various conceptions of truth (bivalent, multi-valent, degrees of truth, etc.) with corresponding conceptions of inference. The mind figures out the appropriate logic for a given puzzle, and then works within that framework. "Just as in visual information processing, mathematical structure (edges etc.) must be imposed upon the retinal array, because this structure is not literally present in the data, so some logical form must be imposed on a problem requiring reasoning before the actual reasoning can take place" (p. 16). Just as cognitive scientists can study how vision involves the imposition of edges, cognitive scientists can also study how reasoning involves the imposition of logical forms. For example, one does not apply bivalent logic to many contexts of medical reasoning, since medicine uses vague (small, chronic, bluish, painful) as well as probabilistic terms (usually, common, infrequently, may occur). One requires, rather, some form of fuzzy and probabilistic logic in medicine.

This task relativity clashes with the work of philosophers, such as Gilbert Ryle, who take logic to be topic neutral. Topic neutrality was also assumed by the psychologists Peter Wason and Keith Stanovich who considered the inference rules of bivalent, extensional logic, to apply to all reasoning tasks. Notoriously, Wason and his colleagues performed studies supposedly showing that humans are not very rational, since we often fail to live up to those rules. Stenning and van Lambalgen question whether it is always appropriate to apply these rules, and argue that part of the reasoning task is choosing from an inventory of available logics. As discussed at great length in Human Reasoning and Cognitive Science, dialogs with subjects performing the Wason selection task, and similar reasoning tests, show that subjects have difficulty knowing which logic to apply. This is evidently due to the fact that the test, in its original form, contains few clues to help one resolve the matter. In many cases, subjects clearly opt for some non-classical logic or other, and hence their "failure" to live up to the standards of classical logic may not constitute irrationality after all. It simply reflects the choice of another logic. When the intended logic is made clear to the subject, performance dramatically improves.

"Logic is very much task-relative. Consider a mathematical example: if the task is to prove existence theorems with algorithmic content, one uses intuitionistic logic; however, if one is satisfied with abstract existence, classical logic suffices" (p. 350). A given logical form is a tool chosen for its usefulness, that choice itself being a crucial part of reasoning. Many philosophers of logic will insist that they already know this, and there is an unmistakably Wittgensteinian flavor to their approach. One of the authors' illustrations, the long discussion of different possible logical forms for conditionals (pp. 83f), is similar to examples found in logic textbooks which sometimes distinguish different interpretations of the conditional surface form. Advanced logic textbooks typically contrast various logics, such as relevantistic, temporal, etc. Different logics are appropriate for different domains; e.g., deontic logic is more suitable to a normative domain than many other logics. Despite the criticism of Ryle, the primary target of the book appears to be those psychologists who have naively taken for granted a monolithic conception of logic and a narrow view of the range of available logical forms. The book, then, turns out to be not so much a rejection of Frege's claim that psychology is irrelevant to logic. It is, rather, a defense of the claim that logic is relevant to psychology. "[W]e claim for logic a much wider role in cognition than is customarily assumed, in a complete reversal of the tendency to push logic to the fringes, …" (p. 347).

According to Stenning and van Lambalgen, "One aim of this book is to present a view of reasoning as consisting of reasoning to and reasoning from an interpretation, and to apply this view to experimental studies on reasoning" (p. 11). More recent work, however, complicates the picture. Non-rational factors sometimes help determine logical form. For example, quantified claims, such as Some mosquitoes carry viruses, tend to be remembered as claims about kinds (i.e., they are remembered as generics), such as Mosquitoes carry viruses (Leslie and Gelman 2011). Attempts to show generics to be implicitly quantified have proven quite torturous, leading to the conclusion that these are two fundamentally different forms of generalization with different logical forms (Liebesman 2011). The memory phenomenon suggests that generics are the less cognitively demanding form, thus being the default form. Note that this is not necessarily irrational but non-rational; it reflects a lack of reasoning rather than a mistake in reasoning. One could perhaps describe the phenomenon as "purely mechanical," reflecting a performance constraint. So, even if Wason was incorrect in judging humans to be largely irrational, Stenning and van Lambalgen may underestimate the degree to which non-rational constraints play a role in determining logical forms.

In support of the claim that human reasoning is often non-classical, while nonetheless rational, a chapter is devoted to experiments involving syllogistic reasoning. Subjects often just don't interpret such tasks in the classical manner intended by psychologists. There are also various factors which enter into subjects' different possible interpretations of logical form in prima facie syllogistic reasoning. The authors also discuss forms of non-classical reasoning which utilize "minimal models." In a minimal model, "roughly speaking, every positive atomic proposition is false which you have no reason to assume to be true" (p. 185). For example, in reading a train schedule, if a departure time is not listed, one assumes that there is no departure at that time. The authors note that assuming a minimal model at least partly obviates the frame problem.

The use of minimal models presupposes "closed-world reasoning," characterized as follows: "it says that if it is impossible to derive a proposition B from the given premises by repeated application of modus ponens, then one may assume B is false" (p. 184). Hence, the addition of new information, such as information added to the train schedule, could force one to revise an earlier inference, i.e. non-monotonicity. The authors hypothesize that closed-world reasoning is an adaptation for planning (pp. 161f), and conjecture that both language (p. 162) and logical reasoning (p. 219) derive from planning. The authors propose a logic system for implementing closed-world reasoning, provide experimental support that people do sometimes reason in agreement with this system (Chap. 7), and discuss a possible neural network for implementing it (Chap. 8). Since closed-world reasoning is not a specific logic, but compatible with numerous logical systems, the emphasis on closed-world reasoning does not clash with the authors' pluralism.

Stenning and van Lambalgen discuss experiments supporting the hypothesis that "Autistic people can apply closed-world reasoning but have a decreased ability in handling exceptions to cases" (p. 267). In other words, autists have trouble with non-monotonic reasoning. Specifically, the difficulty is "in reasoning to an interpretation" (p. 247) involving "exception-tolerant conditionals," the result being "behavioral rigidity and perseverance" (perseveration) (p. 235). Whereas a normal can take exceptions into account, in deciding whether to infer consequent from antecedent, an autist has greater difficulty doing this, thus explaining why autists have trouble with false-belief tasks; a false-belief scenario represents an abnormal circumstance (pp. 251f). The normal, by contrast, knows that the rule If So-and-so recently knew the location of X, then So-and-so will be able to say where X is has exceptions. This is not necessarily meant as an alternative to the view that autists have a theory-of-mind deficit, as the authors point out that difficulty with non-monotonicity could explain the trouble with theory of mind.

A brief review, such as this, cannot do justice to the scope of this book. Suffice it to note that the book also discusses the role of radical altriciality in human uniqueness, evo devo, modularity, the suppression task, conversational implicature, and the hypothetical neurology of autism, among many other things. The book's most serious flaw, and not entirely a bad thing, is the tendency to discuss somewhat tangential issues in great detail. The book is recommended for anyone interested in the psychology of reasoning.

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